In this presentation, we discuss new tools for comparison principles for viscosity solutions to Integro-Differential Hamilton-Jacobi-Bellman equations. The comparison principle is based on a test function framework, that allows for the simultaneous treatment of generators of diffusion as well as jump processes. Additionally incorporating Lyapunov functions, we are able to show comparison in the strict rather than the usual sup-norm topology. We then apply the theory to a variety of parabolic equations and elliptic problems arising from, for instance, optimal control.

Bio: Fabian Fuchs is a Postdoctoral Research Fellow at Luiss Guido Carli. Before, he earned his doctoral degree at the Center of Mathematical Economics at Bielefeld University under the supervision of Prof. Max Nendel and Prof. Frank Riedel. His research interests are in viscosity theory and non-linear semigroups in finite and infinite dimensions and their applications to optimal control.